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Re: it isn't strange?!

• To: mathgroup at smc.vnet.net
• Subject: [mg116126] Re: it isn't strange?!
• From: Derivator <derivatorb at gmail.com>
• Date: Thu, 3 Feb 2011 05:27:38 -0500 (EST)
• References: <iibds7$nnd$1@smc.vnet.net>

On 2 feb, 12:06, olfa <olfa.mra... at yahoo.fr> wrote:
> Hi Mathematica community,
>
> here is my pb:
>
>  input:
> Reduce[Max[a, b] = Max[c, d], c, Reals]
> output:
>  (d < Max[a, b] && c = Max[a, b]) || (d = Max[a, b] &&  c <= Max[a,
> b])
>
> when testing this output with 2 initialisations:
> d = 2  a =  4  b = 3  c = 6  here d < Max[4, 3] but c is not equal to
> Max[4, 3]
>
> d = 4  a =   4  b = 3  c = 6  here d = Max[4, 3] but c is not <= to
> Max[4, 3]
>
> where is the pb?!

Actually I cannot see any problem. In the examples you give the
initial proposition Max[a, b] == Max[c, d] is false, and the
equivalent proposition generated by Reduce is equally false. If you
consider all possible situations you will find that Max[a, b] ==
Max[c, d] is indeed always equivalent to  (d <= Max[a, b] && c ==
Max[a, b]) || (d == Max[a, b] &&  c <= Max[a,b]): both are
simultaneously true of false. Note that you do not really use a and b
separately, only the combination Max[a,b], so you need to consider
only if  (m == Max[c, d]) is equivalent to (d < m && c == m) || (d ==
m &&  c <= m).
Good luck
L.L.